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## Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Many of these puzzles also appear in Braingle's own collection.

 rec.puzzles Newsgroup FAQ Hall of Fame alt.brain.teasers Newsgroup FAQ
Categories : pickover : pickover.08.p

```Title: Cliff Puzzle 8: Squares and Squares and Squares ....
From: cliff@watson.ibm.com

If you respond to this puzzle, if possible please send me your name,
you provide unique information.  PLEASE ALSO directly mail me a copy of
your response in addition to any responding you do in the newsgroup.  I
will assume it is OK to describe your answer in any article or
publication I may write in the future, with attribution to you, unless
you state otherwise.  Thanks, Cliff Pickover

* * *

1.  What is the smallest square with leading digit 1 which remains a
square when the leading 1 is replaced by a 2?

In other words, if x**2 = 1.........., is there a y**2 = 2.........  ?

2.  What is the smallest square with leading digit 1 which remains a
square when the leading 1 is replaced by a 2 and also remains a square
when the leading digit is replaced by a 3?

3.  What is the smallest square with leading digit 1 which remains a
square when the leading 1 is replaced by a 2, and also remains a square
when the leading digit is replaced by a 3, and also remains a square
when the leading digit is replaced by a 4?
```

Solution
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